Class #26
Civil Engineering Materials – CIVE 2110
Concrete Material
Concrete Compressive Strength, f’c
Cracking
Aging, Maturity
Fall 2010
Dr. Gupta
Dr. Pickett
1
Cracking & Failure Mechanisms
 ApC
Concrete cracking process;
- In a Cylinder:
(MacGregor, 5th ed., pp. 41-43)
- Compressive and Tensile strains are constant,
- In a Beam:
- Compressive and Tensile strains vary with depth,
- load is transferred to concrete having lower strain,
- larger mass of concrete at lower strain,
slows the growth of micro-cracks,
- this reduces Unstable Crack Propagation.
 ApC
 Compressio n
 Tension
2
Cracking & Failure Mechanisms
Strength of concrete in a structure is lower
than that of cylinder because of;
-
Different strain gradients, previous page,
Different placing, compaction, & curing procedures,
Size and shape effects,
-
-
 ApC
Beams are deeper than cylinders,
- Water rises to the top,
- More voids at top,
- Greater compaction at beam bottom
 ApC
Drilled cores can be ≈ 0.85 f’c , because coring process relieves some stress.
 Compressio n
 Tension
3
Core Tests & Equivalent In-Place Strength
Cores are drilled, capped, then tested in same

manner as poured cylinders;
(ASTM C42; ACI 318, section 5.6.5.4);
ApC
-
-
-
-
Water cooled drill-bit produces moisture gradient,
- Wet outside surface, dry interior of core sample,
Moisture gradient causes stress gradient,
- Reduces apparent test strength of core,
 ApC
Must test cores between 48 hours and 7 days after drilling,
- Moisture gradient dissipates after 48 hours,
Core size; - core diameter ≥ 3(max. size of aggregate)
- core length = (1.02.0)diameter of core
Concrete is structurally adequate if; (ACI 318, Sect. 5.6.5.4)
-
Average of 3 cores ≥ 0.85 f c' (MacGregor advises taking 6 cores)
No single core < 0.75 f c'
4
Core Tests & Equivalent In-Place Strength
In-place strength ≠ (core strength)/0.85 ;
MacGregor proposes the following relationships:
'
f ceq
f cis
f cis
scis
f core
= equivalent specified strength, used in design calculations,
= equivalent in-place strength,
= mean equivalent in-place strength,
= standard deviation for equivalent in-place strength,
= core test strength,
2


k1scis 
'
2
f ceq  k2  f cis  1.282
 f cis2 Vl 2/d  Vdia
 Vr2  Vmc2  Vd2
n


f cis  f core Fl / d  Fdia  Fr Fmc  Fd 




5
Core Tests & Equivalent In-Place Strength
f cis  f core Fl / d  Fdia  Fr Fmc  Fd 
Where: f cis = equivalent in-place strength,
f core = core test strength,
Fl / d = correction for length-to-diameter ratio,
Fl / d = 0.87 for l / d = 1.0
Fl / d = 0.93 for l / d = 1.25
Fl / d = 0.96 for l / d = 1.50
Fl / d = 0.98 for l / d = 1.75
Fl / d = 1.0 for l / d = 2.0
Fdia = correction for diameter of core,
Fdia = 1.06, for diameter = 2”
Fdia = 1.00, for diameter = 4”
Fdia = 0.98, for diameter = 6”
Fr = correction for presence of reinforcing bars,
Fr = 1.08, for one bar
Fr = 1.00, for no bars
6
Fr = 1.13, for two bars
Core Tests & Equivalent In-Place Strength
f cis  f core Fl / d  Fdia  Fr Fmc  Fd 
Where: f cis = equivalent in-place strength,
f core = core test strength,
Fmc = accounts for effect of moisture of core at time of test,
Fmc = 1.09, if core was soaked before test,
Fmc = 0.96 if core was air-dried at time of test,
Fd = accounts for damage to the core surface due to drilling,
Fd = 1.06
Factors in:
- 1st parentheses correct strength to that of standard core;
( diameter = 4”, length = 8”, with no rebars )
- 2nd parentheses account for differences between concrete in
7
core vs. concrete in the structure.
Core Tests & Equivalent In-Place Strength
2



k1scis 
'
2
2
2
2
2
2
f ceq  k2  f cis  1.282
 f cis Vl / d  Vdia  Vr  Vmc  Vd 
n


'
Where: f ceq
= equivalent specified strength f cis= mean equivalent in-place strength,


k1 = factor dependent on number of core tests,
k1 = 2.40, for 2 tests
k1 = 1.10, for 8 tests
k1 = 1.47, for 3 tests
k1 = 1.05, for 16 tests
k1 = 1.20, for 5 tests
k1 = 1.03, for 25 tests
k2 = factor dependent on number concrete batches in member or
structure being evaluated,
k2 = 0.90, for cast-in-place member or structure,
containing 1 or many batches
k2 = 0.85, for a precast member or structure
8
n = number of cores,
Core Tests & Equivalent In-Place Strength
2


k1scis 
'
2
f ceq  k2  f cis  1.282
 f cis2 Vl 2/d  Vdia
 Vr2  Vmc2  Vd2
n


Where: f ' = equivalent specified strength
ceq

f cis= mean equivalent in-place strength,
Vl / d =
coefficient of variation due to length/diameter correction,
Vl / d= 0.006, for l / d = 1.5
Vl / d = 0.025, for l / d = 1.0
for l / d = 2.0
Vl / d = 0,
Vdia =
coefficient of variation due to diameter correction,
Vdia = 0, for diameter = 4”
Vdia= 0.12, for diameter = 2”
Vdia = 0.02, for diameter = 6”
Vr =



coefficient of variation due to presence of reinforcing bars in the cores,
Vr = 0, if none of the cores contain bars,
9
Vr = 0.03, if > a third of the cores contain bars,
Core Tests & Equivalent In-Place Strength
2


k1scis 
'
2
f ceq  k2  f cis  1.282
 f cis2 Vl 2/d  Vdia
 Vr2  Vmc2  Vd2
n


'
Where: f ceq
= equivalent specified strength
Vmc =
Vd




f cis= mean equivalent in-place strength,
coefficient of variation due to correction for moisture condition of cores
at time of testing,
Vmc = 0.025,
= coefficient of variation due to damage to cores during drilling,
Vd = 0.025,
If a specific correction factor, Fi  1.0
Then
the corresponding coefficient of variation,
Vi  0
10
Factors Affecting f’c
'
c
Factors Affecting f :









(MacGregor, 5th ed., pp. 44-55)
(1) Water-Cement ratio;
(2) Type of Cement;
(3) Type of Aggregate;
(4) Moisture conditions during Curing;
(5) Temperature during Curing;
(6) Age of Concrete;
(7) Maturity of Concrete;
(8) Rate of Loading;
(1) Water-Cement ratio:

A low Water-Cement ratio produces;



Smaller number of voids after water evaporates,
Larger number of interlocking solids (aggregate),
Increased strength.
11
Factors Affecting f’c

(2) Type of Cement:

Type I, Normal;


Type II, Modified;



compared to Type I;
 gives higher strength, earlier,
 gives higher heat of hydration.
Type IV, Low Heat;



used for moderate exposure to Sulfates,
used to slightly moderate heat of hydration.
Type III, High Early;


used in ordinary construction.
heat of hydration is dissipated slowly,
used in massive structures; dams.
Type V, Sulfate Resisting;

used in foundations, sewers.
(Fig. 3.5, MacGregor, 5th ed.)
12
Factors Affecting f’c

 ApC
(3) Type of Aggregate:

Strength of aggregate;


High strength aggregate gives high f’c .
If aggregate fails before cement-mortar paste,


Size of aggregate;


Larger size gives lower f’c ,
 ApC
 higher interface stress between aggregate and cement-mortar paste.
Texture of aggregate;


Brittle failure occurs.
Rough, angular pieces give high f’c ;
 More interlocking edges.
Grading of aggregate;

Well graded, gives less pores, high f’c ,

Marbles of equal size would easily roll over each other, low f’c .
13
Factors Affecting f’c

(4) Moisture Conditions during Curing:



Prolonged moist curing, gives high f’c ;
Fig. 3-6, MacGregor.
(5) Temperature during Curing:



Colder than 73˚F curing, gives low early, high later, f’c ;
Higher than 73˚F curing, gives high early, low later, f’c ;
Fig. 3-7, MacGregor.
(Fig. 3.7, MacGregor, 5th ed.)
(Fig. 3.6, MacGregor, 5th ed.)
14
Factors Affecting f’c

(6) Age of Concrete:

Older, gives high f’c ;
t


f c'(t )  f c'( 28) 

 4  0.85t 
(t = days of moist curing, 70˚F)
t


'
'
 For Type III cement: f c ( t )  f c ( 28 ) 

 2.3  0.92t 


For Type I cement:
(Fig. 3.8, MacGregor, 5th ed.)
(7) Maturity of Concrete:


Strength is a function of
Time at Temperature ;
Use as a guide to determine
when to remove forms ;
n


n


M   TiF  11 ti    TiC  10 ti 
i 1
TiF  _  F
i 1
during i th int erval
TiC  _ C during i th int erval
ti  num ber of
days at Ti
15
Factors Affecting f’c

(8) Rate of Loading:
(MacGregor, 5th ed., p. 52)
psi

 10
sec
sec .

Standard rate, gives high f’c ; 35

Very much slower rate, gives 0.75 x (standard test strength) ;

Earthquake rate, gives 1.15 x (standard test strength) ;

0.10  0.15 seconds load to failure
30,000
psi

 9,000
sec
sec .
16